THE NULL EFFECT OF CROSS SECTIONS OTHER THAN THE MAXIMUM PITTED CROSS SECTION ON STRENGTH

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THE NULL EFFECT OF CROSS SECTIONS OTHER THAN THE MAXIMUM PITTED CROSS SECTION ON STRENGTH

REDUCTION OF AGED MARINE PLATES SUBJECTED TO UNIAXIAL TENSILE LOADING

Commodore M Munir Hassan (Retd)⁽¹⁾, Tasmia Hoque⁽²⁾ and Lieutenant Colonel Muhammad Rabiul Islam, PhD⁽³⁾

1. Professor, Department of Naval Architecture and Marine Engineering Military Institute of Science and Technology, Dhaka,

E-mail: Bangladesh [email protected]

2. Lecturer, Department of Naval Architecture and Marine Engineering Military Institute of Science and Technology, Dhaka

3. Instructor Class-A, Department of Naval Architecture and Marine Engineering Military Institute of Science and Technology, Dhaka

ABSTRACT

It is of essential importance to predict the strength reduction due to pitting corrosion for a proper condition assessment of aged ships. The crucial location of maximum pitting as well as the heavy unevenness of the metal surface creates reduction due to pitting on the basis of damage intensity where the strength reduction is only a function of maximum !" # "

is carried out where MSC NASTRAN nonlinear implicit analysis code has been used in large deformation analysis of were generated by other researchers using a probabilistic corrosion model.

Key words: Strength Reduction, Pitting Corrosion, MSC NASTRAN, Nonlinear Implicit Analysis, Probabilistic Cor- rosion Mode

1.0 INTRODUCTION

Condition assessment is a very important scheme as many vessels are removed from service before reaching the end of their designed life. A Condition Assessment Program is aimed at determining and assessing the actual technical condition of hull and/or machinery, electrical installation and cargo related systems at a given point of time by surveys and investigations.

The purpose of a Condition Assessment Survey is to analyze the remaining strength of the hull structure.

Corrosion wastage is a prominent cause of age related deterioration of steel structures. Metal degrades locally in pit forms reducing strength and deformability, which are main salient features for integrity of steel structures. For a proper condition assessment of aging ships, it is of essential importance to predict the strength and absorbing energy during collapse and/or fracture of corroded plate [1].

According to Nakai et al. [2] it is very important to on overall strength but also on local strength. They

ISSN 2224-2007

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have investigated shape of corrosion pit on a single hull tanker and found circular cone shaped pit on hold frame of bulk carrier and spherical shaped pit on the not come into play [3]. It is thus of great importance to consider actual shape of pits in study. Paik et al. [4-5] studied the ultimate strength behavior and Sumi [6-7] estimated tensile strength, bending strength and deformability of steel corroded plates considering two types of pit shape. In the present study it is aimed to enhance the periodic survey of Bangladesh marine structure in case of pitted steel plate considering the actual pit shape that observed in Bangladesh marine plate. Strength reduction in a large pitted plate and part of that plate containing maximum pitted cross section is compared by engineering stress strain which is investigated with the help of tensile test by universal testing machine.

2.0 ACTUAL PIT SHAPE OF BANGLADESH MARINE CORRODED PLATE

Munir Hassan investigated the actual pit shape of Bangladesh marine corroded plate in part of his PhD research. He collected a number of pitted plates structures and prepared the surfaces by sand blasting.

! glass. Finally he observed the pit cross section as conical (Fig 1). In this study the same pit shape is considered.

Fig 1. Replication of pitted surface.

The probabilistic corrosion model that was proposed by Yamamoto and Ikegami [8] can quantitatively evaluate generation and progress of corrosion. They estimated parameters governing their probabilistic "

Islam [9] generated data sets by using ‘Monte Carlo Simulation’ and Three-dimensional computer aided design software ‘RHINOCEROS’ [10] was used to model the corrosion surface by the NURBS (Non Uniform Rational B-Spline) surfaces.

# $ selecting a part of total pitted surface which includes the maximum pitted cross section. Here the length of part is chosen as 20 mm [a random choice] [10mm to each side of the maximum pitted cross section].

So the size of the part is 20 x original breadth of the sample and the location of maximum pitted surface is at middle of the part. The original size of the pitted plate specimen is 200 x 38mm. The location of maximum pitted cross section within the total pitted surface is traced by calculating the average % &

of the pitted surface for analysis is 20 x 38mm. The original locations of maximum pitted cross section and cross sections at each side of 10mm is remained '*+

Pit Intensity (DOP: De- gree Of pit Intensity)

Total Pitted Surface

Partial Pitted surface containing the maximum pitted

cross section at middle

DOP 19

DOP 51

DOP 73

DOP 92

Fig 2. Simulation images of pitted surfaces.

3.0 MATERIAL DEFINITION

In this study an elastoplastic material is considered.

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True stress strain curve is produced from engineering stress-strain by using the following simple equation.

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Two types of intact plate, class and local were collected and they were tested by UTM to obtain the engineering stress-strain curve (Fig 4, Fig 5). The chemical composition of the plates was also tested and shown in Table I along with the mechanical properties in Table II.

Fig 3.!

Fig 4. Engineering stress strain curve of local plate.

Fig 5. Engineering stress strain curve of class plate.

In case of large and non-uniform deformation the engineering/nominal quantities of stress and strain are valid up to ultimate limit in their true form and can be calculated from engineering part. That is why, the analysis has been done up to the ultimate limit

in this study. The engineering stress strain has been converted into true stress strain using equation stated

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The true stress strain curve obtained using the

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Fig 6. True stress strain curve of local plate.

Fig 7. True stress strain curve of class plate TABLE I. CHEMICAL COMPOSTION

Material Fe Mn P

LOCAL

PLATE 98.71 0.606 0.19

CLASS

PLATE 99.35 0.426 0.22

TABLE II. MECHANICAL PROPERTIES

Material

Yield Strength

( MPa)

Young's Modulus

(MPa)

Tensile Strength

(MPa) LOCAL

PLATE 316.98 26408.64 537.8 CLASS

PLATE 365.54 30180.03 478.98

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4.0 FINITE ELEMENT MODEL

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by ‘MSC PATRAN – Academic Version’ [11] using 8-node hexahedron elements (Fig 8(a)). The loading condition is uniaxial and static where all the nodes of one end kept constrained in all directions.

The current model was generated for total pitted surface and total surface but partially pitted which contains maximum pitted cross section. Due to the element number limitation in academic version, the minimum size in loading direction could be analyzed is 2 mm. In the case of corroded specimens, a minimum element size 1 mm under the deepest (Figure8(b)).

Fig 8. Finite Element Modeling: (a) Boundary Condition; (b) A mid surface is introduced.

The most reasonable element size 1x1x1mm could not be used due to limitation of academic version and DD model was generated having elements of 2x2x2 mm.

5.0 FINITE ELEMENT ANALYSIS RESULT

The validation of input properties was ensured by the FEA of the intact plate (Fig 9) when output curve form the simulation superimposed on the input stress strain curve (Fig 10: Local Plate).

Fig 9. FEA of intact local plate.

Fig 10. Validation curve of intact local plate properties

Fig 11. FEA of intact class plate.

In the similar manner the class plates were also simulated and they result in superimposition of input !"

were conducted for both pitted surface and partially pitted surface containing maximum pitted cross #!

13(b).

Here the superimposition of two curves indicates that total pitted surface and partially pitted surface absorb equal quantity of load to reach to its ultimate #

Fig 12. Validation curve of intact class plate properties.

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Fig 13. FEA of DOP 19 (a) Total pitted surface, b) Partially pitted surface, (c) output stress strain curve.

The simulations were conducted for both pitted surface and partially pitted surface with maximum of class and local plate. The ultimate stresses are compiled in TABLE III and TABLE IV.

For both type of plate sizes with increasing number of pit intensity. It can be visible from both the table that, for a particular percentage of pitting occurs in a plate, their stress reached to nearly equal ultimate point irrespective of the plate size. Fig 14 to Fig 20 shows the superimpositions of the input and output curves.

TABLE III. COMPARISON BETWEEN ULTIMATE STRESSES OF PITTED SURFACE

AND PARTIALLY PITTED SURFACE ULTIMATE STRESS in MPa (Local Plate)

Pit intensity

DOP 0 (intact plate)

DOP 19

DOP 51

DOP 73

DOP 90 Total pitted

surface 634.24 580.8 514.9 590.59 478.5 Partially pit-

ted surface 634.24 571.3 514.9 485.59 475.8

Fig 14. Comparison of total pitted surface and partially pitted surface with DOP 19 of local plate.

Fig 15. Comparison of total pitted surface and partially pitted surface with DOP 51 of local plate.

Fig 16. Comparison of total pitted surface and partially pitted surface with DOP 73 for local plate

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Fig 17. Comparison of total pitted surface and partially pitted surface with DOP 92 for local plate.

TABLE IV. COMPARISON BETWEEN ULTIMATE STRESSES OF PITTED SURFACE

AND PARTIALLY PITTED SURFACE.

ULTIMATE STRESS in MPa (Class Plate) Pit

intensity

DOP 0 (intact plate)

DOP 19

DOP 51

DOP 73

DOP 92 Total pitted

surface 599.06 540.90 497.14 492.6 455.32 Partially

pitted surface

599.06 541.2 497.14 485.58 452.08

Fig 18. Comparison of total pitted surface and partially pitted surface with DOP 19 for class plate.

Fig 19. Comparison of full pitted surface and plate.

Fig 20. Comparison of total pitted surface and partially pitted surface with DOP 73 for class plate.

Fig 21. Comparison of total pitted surface and partially pitted surface DOP 92 for class plate.

partially pitted surface containing maximum pitted cross sectional area achieves the equal ultimate stress before necking as the total pitted surface does when they are subjected to equal amount of uniaxial tensile loads.

6.0 STRENGTH REDUCTION DUE TO PITTING

structural integrity namely strength reduction been calculated from the simulation results. The stress at ultimate limit has been considered from the strain elongation (from experiment by UTM) of material.

Paik et al. [4] derived an empirical formula for predicting the ultimate compressive strength and shear strength based on minimum cross section of corroded surface considering cylindrical pit shape.

Ru=(1-Dm ) .73

………..……..(1)

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Where Ru is the ultimate strength of pitted plates normalized by that of an intact plate. Which is later on proved by Y Sumi and Ahmmed[6] that the formula is wide applicable in case of conical shape of pits

Dm=(Ao-AP)/Ao

……….. (2)

Where Ao is the intact sectional area and AP is the smallest cross sectional area due to surface pits. However, in this study reduced strength was calculated from the data obtained from simulation and also using the empirical formula given by Paik et al [4] for both local and class plate taking into consideration of total pitted surface and partially pitted surface containing maximum pitted cross section (Table V, Table VI).

TABLE V. Comparison between R_u of Total Pitted Surface and Partially Pitted Surface (Local Plate)

DOP A_p D_m R_u (numeri- cal data)

Calculation of R_u from FE analysis

Total pitted surface

Total sur- face but partially

pitted 19 63.65 0.16 0.88 .91 0.90 51 53.90 0.29 0.78 0.81 0.81 73 49.27 0.35 0.73 0.77 0.76 92 40.22 0.47 0.63 0.75 0.75 TABLE VI. Comparison between R_u of total pitted surface and partially pitted surface (class plate)

DOP A_p D_m R_u (numeri- cal data)

Calculation of R_u from FE analysis

Total pitted surface

Total sur- face but partially

pitted 19 63.65 0.16 0.88 0.90 0.90 51 53.90 0.29 0.78 0.83 0.83 73 49.27 0.35 0.73 0.82 0.81 92 40.22 0.47 0.63 0.76 0.75 reducing in the same pattern for both the pitted surface and partially pitted surface containing maximum pitted cross section. Not only that, they are also nearly equal in magnitude with a variation not more than 6% from the empirical formula.

Fig 22. Comparison between strength reduction determined from analysis result and numerical data.

Fig 23. Comparison between strength reduction determined from analysis result and numerical data.

7.0 DISCUSSION

The marine structures are continuously subjected to corrosive environment during their service. It would be helpful if the characteristics of pitting can be predicted earlier through the survey of the vessels and other marine structures for assessing their condition.

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of maximum pitted ross sectional area on aged marine plate which is subjected to uniaxial tensile loading. From this study, it has been understood that strength reduces and damage increases with increase of degree of pit depth irrespective of their pitting position. The graphical representation shows that Strength reduction factor of total pitted surface and surface containing maximum pitted cross section (partially pitted surface), being analogous in nature and pattern with increase of damage. From this, it can be decided that, only maximum pitted cross section is playing the major role in strength reduction and # $ " $ sections.

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8.0 CONCLUSION

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During the survey it is essential to examine and inspect the condition of the structures which are subjected to pitting corrosion. This study is focused other than the maximum pitted cross section.

It can be concluded that, concentrating only on that cross section during survey of pitted surface is fair enough to assess the structural integrity of the marine aged structures. This will help the ship owner and the for the inspection and prediction of the consequent damage of the structure.

References

[1] Sumi Y, Strength and Deformability of Corroded Steel Plates Estimated by Replicated Specimens (Journal of Ship Production, 24(3), 2008), pp.161-167.

!"#$"%&$"' * Corrosion on Local Strength of Hold Frames of Bulk Carriers (1st report) (Marine Structures, 17, 2004), pp.403-432.

[3] Oka M, Kitada H & Watanabe T : Experimental study on statistical strength of corrosive mild steel, Journal of the Japan Society of Naval Architects and Ocean Engineers, 167, 1990, pp.229-235 (in Japanese).

[4] Paik J K, Lee J M and Ko M J, Ultimate Strength of Plate Elements with Pit Corrosion Wastage (J Engineering for Maritime Environment, Vol.217, 2003), pp.185-200.

[5] Paik, J K, Lee J M & Ko M J: Ultimate shear strength of plate elements with pit corrosion wastage, Thin-Wall Structures, 42, 2004, pp.1161-1176.

[6] Ahmmad Md. M and Sumi Y, Strength and Deformability of Corroded Steel Plates under Quasi-static Tensile Load (J Mar Sci Technol, Vol.15(1), 2010), pp.1-15.

/;#<=<>"? ' *@

Strength and Deformability of Steel Rectangular Plates Subjected to Uniaxial Tension and Pure Bending (jjasnaoe,14, 2011, 9).

[8] Yamamoto N and Ikegami K, A Study on the Degradation of Coating and Corrosion of Ships Hull Based on The Probabilistic

& GX Z # & ' 120, 1998), pp.121-128.

\ ; #< =<" *$^ ? ' Z * Corrosion On Strength And Deformability Of Steel Plate Subjected To Tensile Load And Bending, 2011 .

[10] Robert McNeel and Associates, Rhinoceros user guide: NURBS modeling for Windows. Version 3.0 (McNeel, Seattle, 2003).

[11] Combined Documentation, MD Patran Users Guide (MSC.

Software Corporation, Santa Ana, California, 2006 R